相关论文: Electrostatic models for zeros of polynomials: old…

We study the asymptotic distribution of roots of Lommel polynomials as polynomials of the order with a variable and purely imaginary argument. The roots are complex and accumulate on certain curves in the complex plane. We prove existence…

We give asymptotic approximations of the zeros of certain high degree polynomials. The zeros can be used to compute the filter coefficients in the dilation equations which define the compactly supported orthogonal Daubechies wavelets.…

Let {$\{S_n\}_{n\geqslant 0}$} be the sequence of orthogonal polynomials with respect to the Laguerre-Sobolev inner product $$ \langle f,g\rangle_S =\!\int_{0}^{+\infty}\! f(x)…

A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…

The equations of electrostatics are presented in pre-metric form, and it is pointed out that if the origin of the nonlinearity is the constitutive law for the medium then the differential equations themselves remain linear, while the…

In this paper we investigate the distribution of zeros of Boubaker polynomials.

A new numerical method is introduced for calculation of quasi-polynomial zeros with constant single delay. The trajectories of zeros are obtained depending on time-delay from zero to final time-delay value. The method determines all the…

We will examine the electrostatic properties of exceptional and regular zeros of $X_m$-Laguerre and $X_m$-Jacobi polynomials. Since there is a close connection between the electrostatic properties of the zeros and the stability of…

We survey results on the distribution of zeros of random polynomials and of random holomorphic sections of line bundles, especially for large classes of probability measures on the spaces of holomorphic sections. We provide furthermore some…

In this paper, we study the value distribution of zeros of certain nonlinear difference polynomials of entire functions of finite order.

Recently Brownawell and the second author proved a "non-degenerate" case of the (unproved) "Zilber Nullstellensatz" in connexion with "Strong Exponential Closure". Here we treat some significant new cases. In particular these settle…

In this paper we present a survey about analytic properties of polynomials orthogonal with respect to a weighted Sobolev inner product such that the vector of measures has an unbounded support. In particular, we are focused in the study of…

In this note we extend the classical relation between the equilibrium configurations of unit movable point charges in a plane electrostatic field created by these charges together with some fixed point charges and the polynomial solutions…

The interplay between electrostatic interactions and orientational correlations is studied for a model system of charged rods positioned on a chain, using Monte Carlo simulation techniques. It is shown that the coupling brings about the…

In this paper we study the asymptotic zero distribution of eigenpolynomials for degenerate exactly-solvable operators. We present an explicit conjecture and partial results on the growth of the largest modulus of the roots of the unique and…

This paper revisits the notion of classical orthogonal polynomials from a broader functional-analytic point of view. It is intended neither as a survey of known results nor as a review of the literature, but rather as a conceptual…

In this article we study some classical aspects of Podolsky Electrodynamics in the static regime. We develop the multipole expansion for the theory in both the electrostatic and the magnetostatic cases. We also address the problem of…

We present fully polynomial approximation schemes for a broad class of Holant problems with complex edge weights, which we call Holant polynomials. We transform these problems into partition functions of abstract combinatorial structures…

The recent discovery of electro-active polymers has shown great promises in the field of soft robotics, and was logically followed by experimental, numerical and theoretical developments. Most of these studies were concerned with systems…

Some properties and relations satisfied by the polynomial solutions of a bispectral problem are studied. Given a finite order differential operator, under certain restrictions, its polynomial eigenfunctions are explicitly obtained, as well…